# Rate of Change and Slope Worksheets

We can use the graph to visually represent the values in a data set, which helps us in identifying the different patterns and trends in it. We can calculate the mid-points of a line and even determine the equation that represents a data set. Moreover, we can even use a graph to find the distance between two points. We can use a graph to determine the rate of change from a graph. The rate of change that we generally refer to as the slope can be determined using the ratio between rise and run. You have to divide the change in the vertical values by the change in the horizontal values. The formula for the rate of change using a graph is given by; m=((y_{2} - y_{1}))/((x_{2} - x_{1})). These worksheets help students understand the meaning of rate of change in the terms of what they are trying to evaluate.

### Aligned Standard: HSS-ID.C.7

- Milky Problem Step-by-step Lesson- See if you can make sense of how Andrew drinks milk.
- Guided Lesson - Renting a motorcycle, gaining weight, and baking cupcakes.
- Guided Lesson Explanation - It is interesting how sometimes you can ballpark your answer from the get go with these problems.
- Practice Worksheet - I was baby sitting while writing this one! I had the kids help me come up with all the story lines.
- Matching Worksheet - The kids went to bed when I wrote this one. Does it lack imagination?

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

We try to form the problems in many different ways with this one.

- Homework 1 - Andy had 7 liters of water in his jug. He was making ice tea at the rate of 4 liters of ice tea in 3 hours. He had 3 liters of water left. How much water does Andy use each hour?
- Homework 2 - Max is charged $70 and an additional $0.20 per mile for the car that he rented. Represent the cost of car if it was driven 80 miles with an equation.
- Homework 3 - Flora uses 10 kg of potatoes for making chips. She uses an additional 2 kg of potatoes for each person that will be eating chips. Write an equation to express the use of potatoes for making chips.

### Practice Worksheets

You need to represent an interpret slope within the context of the problems.

- Practice 1 - Sara was buying makeup that she needed very quickly. The one day mailing charge was $50. Her mascara were $2.20 each.
- Practice 2 - George's weight is 80 kg. He wants to decrease his weight so he starts exercise daily. After 2 weeks he was 60 kg.
- Practice 3 - Rex owns a strawberry farm. On Monday he had already picked 70 kg of strawberries. By the end of Friday, Rex had picked a total of 122 kg of strawberries. How many strawberries was Rex picking, on average, Tuesday - Friday?

### Math Skill Quizzes

We track the growth or loss within rate for problems here.

- Quiz 1 - Dizzy has 15 fresh flowers. After 2 hours, she had 12 fresh flowers. Describe the relationship between time and fresh flowers.
- Quiz 2 - Frido used 6 packs of pens this week because it was a busy week. Normal he uses 2 packets every week. How many packs of pens would you expect Frido to use this month (4 weeks)?
- Quiz 3 - Karen has 12 dolls. She makes her own dolls. She uses 45 cm of thread to make 3 dolls. 2 months later Karen doll collection grows to 23 dolls. How much thread did she use?

### What Does the Slope of a Graph Tell Us?

Visualizations are powerful and effective tools for making complex information easy to understand. Ultimately, they can inspire more engaging and capable relationships with customers through their ability to provide clarity and context. To create a graph, however, you must have data. Unfortunately, the default methods for gathering data are often time-consuming, prompting a need for innovation.

Graphs are a visual representation of information, typically used to show relationships between different data sets. There are hundreds of different graphs and graphing techniques with different purposes and outcomes.

The slope is an important term used with equations and graphs. On a graph it represents a measure of the change in the vertical distance between a series of measurements taken along the same line. So, if you have a graph about weight loss with weight plotted on the y axis, the slope will tell you how fast the weight changes over time.

### What Does a Slope Represent?

It is a rate of change of something (e.g., height, voltage, temperature, time) in coordinates; as one unit of measurement goes up, the next goes down. In other words, slope measures the change in the dependent variable according to the changes observed in an independent variable. The line gets steeper as the slope increases.

A steep slope represents many changes in a finite time; therefore, it is called clutter. A gradual slope can be associated with a more gradual increase in order. The steep slope is associated with more radical changes in language, and the gradual slope is associated with more progressive changes.

It can tell us how demand varies in response to pricing, how quickly sales are increasing, or simply how expenditure changes in response to income changes. Let's see how an equation of a graph represents a slope: y = bx + c, where b represents the slope, and the formula to depict it is: slope = change in y/change in x.

Another point to remember is whenever the slope is positive, the line goes up from left to right. However, the line goes down from left to right in a negative slope.

### Determine the Slope of a Graph

When an object travels in a concave shape with a variable speed, the portion of its trajectory below the surface will rise higher than the portion above the surface.

With the help of a graph, you can easily determine the slope if you have the two points, rise and run. But the question is how to find these points?

**Example: Find the slope of a line with the help of these points (4,2) and (5,5).**

**Solution:** The steps will still be the same, and we don’t have to look for points in a graph.

Let's name the coordinates in these points. x_{1} = 4, x_{2} = 5, y_{1} = 2 and y_{1} = 5. The slope is denoted by m, and the formula is:

m=((y_{2} - y_{1}))/((x_{2} - x_{1}))

After placing the values, you’ll get m = 5-2/5-4. Therefore, m = 3.

Consider the same points, but now the points are reversed. The points of line 1 are (5,5), and line 2 are (4,2).

Same procedure will be followed here and the sequence of points will be x_{1} = 5, x_{2} = 4, y_{1} = 5 and y_{1} = 2. It will be:

m = 2 - 5/ 4 - 5, m = 3.

The point of this example is to explain that even if we reverse the order pairs, the slope will remain to be the same.

The steepness of a graph is described by its slope. As we have seen, this value of a graph remains the same along the line. Moreover, you can find the slope of a graph in two ways, by either looking at the graph or using the coordinates.